Asymptotic structure of the spectrum in a dirichlet-strip with double periodic perforations

Sergei A. Nazarov, Rafael Orive-Illera, Maria-Eugenia Perez-Martinez

Результат исследований: Научные публикации в периодических изданияхстатья

Выдержка

We address a spectral problem for the Dirichlet-Laplace operator in a waveguide II ε. II ε is obtained from an unbounded two-dimensional strip II which is periodically perforated by a family of holes, which are also periodically distributed along a line, the so-called "perforation string". We assume that the two periods are different, namely, O(1) and O( ε) respectively, where 0 < ε ≪ 1. We look at the band-gap structure of the spectrum σ ε as ε → 0. We derive asymptotic formulas for the endpoints of the spectral bands and show that σ ε has a large number of short bands of length O( ε) which alternate with wide gaps of width O(1).

Язык оригиналаанглийский
Страницы (с-по)733–757
ЖурналNetworks and Heterogeneous Media
Том14
Номер выпуска4
DOI
СостояниеОпубликовано - 2019

Отпечаток

Dirichlet
Strip
Energy gap
Waveguides
Spectral Problem
Laplace Operator
Band Gap
Asymptotic Formula
Alternate
Waveguide
Strings
Line
Family

Предметные области Scopus

  • Теория вероятности и статистика
  • Технология (все)
  • Прикладные компьютерные науки
  • Прикладная математика

Цитировать

Nazarov, Sergei A. ; Orive-Illera, Rafael ; Perez-Martinez, Maria-Eugenia. / Asymptotic structure of the spectrum in a dirichlet-strip with double periodic perforations. В: Networks and Heterogeneous Media. 2019 ; Том 14, № 4. стр. 733–757.
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year = "2019",
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Asymptotic structure of the spectrum in a dirichlet-strip with double periodic perforations. / Nazarov, Sergei A. ; Orive-Illera, Rafael; Perez-Martinez, Maria-Eugenia.

В: Networks and Heterogeneous Media, Том 14, № 4, 2019, стр. 733–757.

Результат исследований: Научные публикации в периодических изданияхстатья

TY - JOUR

T1 - Asymptotic structure of the spectrum in a dirichlet-strip with double periodic perforations

AU - Nazarov, Sergei A.

AU - Orive-Illera, Rafael

AU - Perez-Martinez, Maria-Eugenia

PY - 2019

Y1 - 2019

N2 - We address a spectral problem for the Dirichlet-Laplace operator in a waveguide II ε. II ε is obtained from an unbounded two-dimensional strip II which is periodically perforated by a family of holes, which are also periodically distributed along a line, the so-called "perforation string". We assume that the two periods are different, namely, O(1) and O( ε) respectively, where 0 < ε ≪ 1. We look at the band-gap structure of the spectrum σ ε as ε → 0. We derive asymptotic formulas for the endpoints of the spectral bands and show that σ ε has a large number of short bands of length O( ε) which alternate with wide gaps of width O(1).

AB - We address a spectral problem for the Dirichlet-Laplace operator in a waveguide II ε. II ε is obtained from an unbounded two-dimensional strip II which is periodically perforated by a family of holes, which are also periodically distributed along a line, the so-called "perforation string". We assume that the two periods are different, namely, O(1) and O( ε) respectively, where 0 < ε ≪ 1. We look at the band-gap structure of the spectrum σ ε as ε → 0. We derive asymptotic formulas for the endpoints of the spectral bands and show that σ ε has a large number of short bands of length O( ε) which alternate with wide gaps of width O(1).

KW - Band-gap structure

KW - Dirichlet-Laplace operator

KW - Double periodicity

KW - Homogenization

KW - Perforated media

KW - Spectral perturbations

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DO - 10.3934/nhm.2019029

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